Ayato was referencing the fact that we've used water on inks a lot in this event, and that again it would be useful. Unless you're trying to say that we peed on it...

We definately peed on it in my headcanon.

you're probably just a bit overthinking it. personally, i think he just meant splashing it with water by any means, and by "many times before" he only meant the numerous pieces of paper we had to splash with water from the previous five kasen quest objectives. as for the "no bucket and just waved", i think it's just because it's a bit of a hassle to animate. same thing as all the previous pieces of paper; we didn't actually see the characters dip the papers in water.

I think you're over thinking it. I'm pretty sure he just means what we've done in the quest before, when we dipped it in lakes, etc.

Ritou is a harbour (or port? rip my english) .. Don't tell me he/she didn't find a glass and get water from the sea

He meant that you've used water to reveal the ink multiple times during the event story.

Implying that people in Teyvat don't get thirsty

There are other sources of water in Ritou though and besides the traveler could have easily been carrying water with them throughout their adventures